260 Mr. C. Spurge. On the Effect of Polish on the 



Table VII shows us that the effect of polishing is to decrease I from 

 108-088° to 107-819°, a diminution of 0'269°. Since then a rotation of 

 4° 27' produces an increase of 0'166 ; to produce an effect equal to that 

 of polishing by rotation, the crystal face would have to be rotated in 

 its own plane 8°. No such error of setting was possible. 



Again, 



r'-r = 94-137°, and E/-R = 91-665°. 



The last reading is of an altogether different magnitude to what 

 has hitherto occurred. 



A template was constructed and used in future observations to test 

 the accuracy of setting. It was found that the setting by the screens 

 was always correct on afterwards being examined by the template, 

 and when it was out of adjustment by the screens the template did 

 not fit. These three grounds seem to be more than sufficient for the 

 rejection of the hypothesis of a rotation of the crystal face in its own 

 plane. 



It may be of some interest to calculate the value of the change in 

 the ratio of the axes produced by a rotation of 4° 27'. We therefore 

 calculate it — 



Thus cos 2*r = — — hl cat , , 



sin 91*665 



whence nr = 1° 53'6', 



and tan *r = 0-03305. 



The value before rotation was 



tan v = 0-02655. 



XIV. Determination of the Effect of Bepolishing the same Face of the 

 Crystal. Investigation of the Errors of Means of a Series of Obser- 

 vations with an Elliptic or Simple Analyser. Comparison of the 

 Relative Accuracy of the Elliptic and Simple Analysers. 



Much of the value of the observations on polishing must depend 

 on the fact whether the crystal can be polished in the same manner, 

 that is, polished and repolished so as to obtain the same results. The 

 crystal was, therefore, submitted to the same process of polishing as 

 has been described already in Section VI. The observations with the 

 same face thus repolished are recorded in Table XII. 



